Comcast channels and Broadband

I have had the basic cable package from Comcast for ~10 years. Until a month ago I received about 70 channels, then I got a digital TV screen (need cable box) on about a third of the channels (TBS, scifi, etc). My wife called comcast to see what we needed to do and they said we were only supposed to be getting 29 channels based on our cheapo ($14) package and it was a mistake that we got the others, then later that day another third of he channels just went away so now we only have the 29 channels.

I can understand how some of the "digital" channels went away but I am puzzled about how the 2nd set of channels went away (they dont have the digital messge - just blank now). I have no cable box, never have.

Lastly, I have broadband from comcast too (I own the modem), coming in from the same cable, if I cancelled my cable TV completely and kept the broadband won't I still see the 29 channels?